Approximation of Pattern Transformation Manifolds with Parametric Dictionaries

The construction of low-dimensional models explaining high-dimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by in-plane geometric transformations of 2D visual patterns. We propose a method for computing a manifold by building a representative pattern such that its transformation manifold accurately fits a set of given observations. We present a solution for the progressive construction of the representative pattern with the aid of a parametric dictionary, which in turn provides an analytical representation of the data and the manifold. Experimental results show that the patterns learned with the proposed algorithm can efficiently capture the main characteristics of the input data with high approximation accuracy, where the invariance to the geometric transformations of the data is accomplished due to the transformation manifold model.